Question

A surveyor measures the angle of elevation to the top of a building to be 70 degrees. The surveyor then walks 50 ft farther from the base of the tower and measures the angle of elevation to be 50 degrees. The surveyor's angle-measuring device 5.5 ft from the ground. How tall is the building, to the nearest foot?

Answer 1

43.804 ft

Working;
Start by drawing the diagram as shown in the attached diagram;
Then use the following trigonometric relations;
Tan (50)= $\frac{h}{50+x}$
Tan (70)=$\frac{h}{x}$

You can then use the value of x to find the value of h. Then add 5.5 ft to h to get height of the building

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Answer 2

Answer:

height of building,H = 5.5 ft + 105.2 ft = 111 ft to the nearest ft.

Step-by-step explanation:

in this question we have given angle of elevation=$70^o$

when surveyor walks 50m farther from the base of the tower that time angle of elevation=$50^o$

As shown in figure in triangle ABD

$Tan (70)= \frac{h}{x}$ .............(1)

or h=2.74x

and in triangle ABC

$Tan (50)= \frac{h}{50+x}$ ...........(2)

put value of h in equation 2

we got,

$1.19= \frac{2.74x}{50+x}$

$(50+x)1.19=2.74x\\50\times 1.19+1.19x-2.74x=0\\59.5-1.55x=0\\59.5=1.55x\\x=38.39ft$

therefore,

Height of the tower is,h=2.74\times 38.39ft

h=105.2ft

Therefore,

height of building,H = 5.5 ft + 105.2 ft = 111 ft to the nearest ft.